A car makes a trip due north for three-fourths of the time and due south one-fourth of the time. The average northward velocity has a magnitude of 31 m/s, and the average southward velocity has a magnitude of 43 m/s. Taking northward to be the positive direction, what is the average velocity for the trip?

The average speed is 34 m/s

Explanation:

The average speed a body is defined for the total distance traveled between the total time

Let's calculate the distance the car travels.

X = V t

Northward

X1 = 31 ¾ t

To the south

X2 = 43 ¼ t

The total distance and time are, we can add the distance as scalars by the movement being on the same North-South line

Xt = X1 + X2

t all = ¾ t + ¼ t = t

Xt = 31 ¾ t + 43 ¼ t

Xt = t (23.25 + 10.75)

Xt = t (34)

We calculate the average speed

V = t 34 / t

V = 34 m / s

The average speed is 34 m / s